The results are presented of studying a mathematical model of linear biomolecular synthesis which accounts for the reversibility of attaching a monomer to a growing molecule and some spontaneous termination of the synthesis. A previous model of a synthesis ignored the influence of reversibility and sinks. It is shown that if the rate of the monomer attachment (the direct process) exceeds the rate of the monomer removal (the reverse process) then the passage to the limit model with infinitely many stages leads to a delay differential equation. For any other ratios of the rates, the solution reaches a stationary state.